Will knee stability improve after a severe knee sprain? my knee buckles inwards and is still unstable after 4 days, even though pain is almost gone.

Time Heals: Ligament and tendon sprain (as in the knee) can take months to heal. After ensuring that you have no major tears of meniscus or ligaments, you will benefit from using a brace (the otc elastic kind may be sufficient) - this will help stabilize the joint allowing better healing. Range of motion exercise, but but heavy exercise will benefit. Easy does it !